In really dirty water you just can't avoid lighting up the stuff in the water. What you can do is make it blend in to the lighter background. Shoot up towards the surface and play with shutter speed for more or less ambient exposure.

Actually I just worked it out.Use the "media" tags around the full link to your video

The video above shows my tripod made from my existing strobe clamps and arms, attached to 3 Sea and Sea 1" ball adapters bolted to the Ike tray. Picture below.Had to enlarge holes to 8mm on 2 adapters, and drill one hole in the tray to attach the third adapter.